Method and system for fluid flow rate measurement

ABSTRACT

A fluid flow meter system for monitoring fluid flow through a lumen includes a first ultrasonic transducer configured to transmit one or more versions of a transmit (TX) signal through a fluid flowing within the lumen, and a second ultrasonic transducer configured to receive one or more respective receive (RX) signals. The fluid flow meter system includes an analog-to-digital converter (ADC) configured to sample, at a first frequency, the one or more RX ultrasonic signals and a processor configured to generate a fine resolution signal based on the one or more RX ultrasonic signals. The fine resolution signal is associated with a second sampling rate higher than the first sampling rate. The processor is also configured to compute a cross-correlation signal indicative of cross-correlation between the fine resolution signal and a waveform and determine an estimated fluid flow parameter based on the computed cross-correlation signal.

RELATED APPLICATION

This application claims priority to U.S. patent application Ser. No.14/741,124, entitled “METHOD AND SYSTEM FOR FLUID FLOW RATE MEASUREMENT”and filed on Jun. 16, 2015, which claims priority to U.S. ProvisionalApplication No. 62/162,568, entitled “METHOD AND SYSTEM FOR FLUID FLOWRATE MEASUREMENT” and filed on May 15, 2015, both of which areincorporated herein by reference in their entirety.

BACKGROUND

Monitoring fluid flow rate in fluid distribution system can allow forpump efficiency (such as in systems employing pumps), leak detection orremote monitoring of fluid distribution systems. In water distributionsystems, monitoring water flow rate can help monitoring water usage anddetecting water leaks. When water leaks are detected at an early stage,substantial damage to buildings can be avoided. In natural gasdistribution system, reliable leak detection can help avoid dangerousfires and/or explosions.

SUMMARY

According to at least one aspect, a fluid flow meter system formonitoring fluid flow through a lumen includes an ultrasonic sensor. Theultrasonic sensor can include a first ultrasonic transducer configuredto transmit one or more versions of a transmit (TX) ultrasonic signalthrough a fluid flowing within the lumen, and a second ultrasonictransducer configured to receive one or more receive (RX) ultrasonicsignals corresponding to the one or more transmitted versions of the TXultrasonic signal. The fluid flow meter system includes ananalog-to-digital converter (ADC) configured to sample, at a firstfrequency, the one or more RX ultrasonic signals received by the secondtransducer. The fluid flow meter system also includes a processorconfigured to generate a fine resolution signal based on the one or moreRX ultrasonic signals. The fine resolution signal is associated with asecond sampling rate higher than the first sampling rate. The processoris also configured to compute a cross-correlation signal indicative ofcross-correlation between the fine resolution signal and a waveform anddetermine an estimated fluid flow rate (or fluid flow velocity) of thefluid based on the computed cross-correlation signal.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a diagram illustrating a flow meter system mounted on apipe.

FIG. 2 is a flow diagram illustrating a method for estimating fluid flowrate or fluid flow velocity.

FIG. 3 is a diagram illustrating different implementations of copies orversions of a transmit (TX) signal for transmission within a given timeperiod.

FIGS. 4A-4C show simulation results illustrating behavior ofdifferential propagation times between downstream and upstream TXsignals in a zero-flow fluid with and without jitter delays.

FIG. 5 is a diagram illustrating a process of interleaving samples frommultiple received RX signals to generate a respective higher resolutioninterleaved signal.

FIG. 6 is a diagram illustrating a process of up-sampling a digitalsignal associated with one or more ADC-sampled RX signals to generate arespective higher resolution up-sampled RX signal.

FIG. 7 shows experimental results for measured differential propagationtimes using up-sampled RX signals.

FIG. 8A shows a block diagram illustrating a process 800 of estimating atime shift between a reference waveform and a fine resolution RX signalbased on partial cross-correlation signal(s).

FIG. 8B shows an illustration of the first and second cross correlationsignals.

FIG. 8C shows a cross-correlation plot and a state machine diagramillustrating a process for determining a cross-correlation peak valueassociated with a respective time window.

FIG. 8D is a diagram illustrating a ternary search for locating afeature value (such as local maximum or local minimum) within a timewindow.

FIG. 9 shows a block diagram illustrating another method for estimatingfluid flow rate (or fluid flow velocity) based on recorded ultrasonicsignals.

DETAILED DESCRIPTION

Systems and devices described in the current disclosure allow foraccurate and cost effective estimation of flow rate (or flowvelocity/speed) for a fluid flowing through a lumen such as a pipe. Inparticular, an ultrasonic fluid flow meter can include ultrasonictransducers capable of transmitting/receiving ultrasonic signals topropagate through the fluid flowing in the lumen. The ultrasonic flowmeter can estimate the fluid flow rate (or fluid flow velocity) based onmeasured or estimated propagation characteristics of the ultrasonicsignal within the fluid. The ultrasonic signal propagation speed (orpropagation time) can vary depending on the type of fluid, fluid flowdirection and speed with respect to signal propagation direction, fluidtemperature, or other fluid parameters that can affect fluid density orfluid compressibility.

An ultrasonic signal propagating in the same direction as a fluid flow(i.e., downstream) propagates faster than another ultrasonic signalpropagating opposite to fluid flow direction (i.e. upstream) or fasterthan an ultrasonic signal propagating in non-moving fluid. Fluid flowspeed (or fluid flow rate) can be estimated based on difference(s) inultrasonic signal propagation time (or difference in ultrasonic signalpropagation speed) between signals propagating differently with respectto fluid flow. For instance, the difference in ultrasonic signalpropagation speed in water between an upstream propagating signal and adownstream propagating signal is linearly proportional to the water flowrate at least for a practical range of water flow rates.

Fluid flow speed (or fluid flow rate) can be estimated based on relativetime delays associated with signals propagating differently (e.g.,upstream and downstream signal) with respect to fluid flow in the lumen.Such relative time delays can be, in some cases, in the range ofnano-seconds (ns). In order to accurately measure (or estimate) therelative time delays between ultrasonic signals, a flow meter can employmultiple analog-to-digital converters (ADCs) with respective ADC clocksrunning at relative time delays with respect to each other. The flowmeter can interleave samples provided by separate ADCs to achieve aneffective sampling rate for measured ultrasonic signals high enough toallow measuring relatively small time delays (such as in the range ofnano-seconds). Using multiple ADCs increases the cost of the flow meterand poses technical challenges such as power efficiency and addressingmismatch in voltage offset between different ADCs. A flow meter also canemploy a single high speed ADC to improve signal resolution. However,high speed ADCs are more expensive and consume significantly more powerthan ADCs with lower sampling rates. Also, employing a high speed ADCmay not be enough to reach a given desired signal resolution.

FIG. 1 shows a diagram illustrating a flow meter system 100 mounted on apipe 10. The flow rate meter system 100 includes two ultrasonictransducers 110 a and 110 b (also referred to either individually orcollectively as transducer(s) 110), two waveguides 120 a and 120 b (alsoreferred to either individually or collectively as waveguide(s) 120), acontrol circuit 150 coupled to the ultrasonic transducers 110 and atransducer block 130 for fixing the ultrasonic transducers 110 to thepipe 10. The control circuit 150 can include a processor 151 and ananalog-to-digital converter (ADC) 155.

As shown in FIG. 1, the ultrasonic transducers 110 can be mounted in anon-invasive manner. In such configuration, the ultrasonic transducers110 or the waveguides 120 do not interfere with the fluid flow pathwithin the pipe 10. The ultrasonic transducers 110 or the waveguides 120can be mounted on the pipe 10 without cutting or grooving the pipe 10.In an invasive configuration, the transducers 110 can be placed withinopenings of the pipe wall 11. The waveguides 120 can be optional. Assuch, the transducers 110 can be mounted to be directly in contact with,or close proximity to, the pipe 10 without waveguides 120.

Each of the ultrasonic transducers 110 can be capable of transmittingand receiving ultrasonic signals. For instance, the ultrasonictransducer 110 a transmits the ultrasonic signal 101 a, which propagatesthrough the waveguide 120 a into the pipe 10, reflects back from thepipe wall 11 towards the waveguide 120 b and is received at theultrasonic transducer 110 b. The ultrasonic transducer 110 b transmitsthe ultrasonic signal 101 b, which propagates through the waveguide 120b into the pipe 10, reflects back from the pipe wall 11 towards thewaveguide 120 a and is received at the ultrasonic transducer 110 a. Inthe pipe 10, fluid is flowing according to direction 12. As such, theultrasonic signal 101 a propagates upstream (i.e., having a motioncomponent along the axis of the pipe 10 with a direction opposite to thefluid flow direction 12) within the pipe 10 and the ultrasonic signal101 b propagates downstream (i.e., having a motion component along theaxis of the pipe 10 with a direction similar to the fluid flow direction12). Given the propagation direction of the ultrasonic signals 101 a and101 b with respect to the fluid flow direction 12, the respectivepropagation times are affected differently by the fluid flow. Forinstance, the propagation time of the downstream ultrasonic signal 101 bis expected to be shorter than that of the downstream ultrasonic signal101 a. Ultrasonic signals propagating through the fluid are alsoreferred to herein as ultrasonic signal(s) 101.

In some implementations, the ultrasonic transducers 110 can transmitsignals in one direction (e.g., downstream or upstream). The processor151 can compare signal propagation time of a downstream or upstreamultrasonic signal to propagation time associated with a signalpropagating in non-moving fluid to determine the effect of fluid flow onsignal propagation through the fluid. Also, while FIG. 1 shows anillustrative configuration of mounting the transducers 110 on the pipe10, other configurations are contemplated by the current disclosure. Forinstance, the transducers 110 can be mounted across one another on thepipe 10, at an angle with respect to the longitudinal axis of the pipesuch that the ultrasonic signals 101 can propagate between thetransducers 110 without necessarily bouncing off the pipe wall 11 (e.g.,propagating in a straight line between the transducers 101).

In some implementations, the flow meter system 100 can include more thantwo ultrasonic transducers 110. Each ultrasonic transducer 110 in theflow meter system 100 can be capable of acting as a transmitter and areceiver. Some ultrasonic transducers 110 in the flow meter system 100can be configured (or designated) to act as transmitters while otherscan be configured (or designated) to act as receivers. While the system100 employs the ultrasonic transducers 110 to transmit or receivesignals, other types of signal transmitters/receivers such as acousticor electromagnetic transmitters/receivers can be employed.

The ADC 155 can be configured to sample receive (RX) ultrasonic signalsreceived at the ultrasonic transducers 110. The flow meter system 100includes a single ADC converter 155. The sampling rate of the ADC 155can be smaller than a sampling rate associated with a desired signalresolution (or desired sampling rate) for achieving accurate estimationof fluid flow rate, fluid flow speed, or relative time delays associatedwith received (RX) ultrasonic signals. For instance, the sampling periodof the ADC 155 can be in the range of micro-seconds (μs) while a desiredresolution of relative time delays between ultrasonic signals 101propagating within the fluid can be in the range of nano-seconds (ns).In particular, accurate estimation of fluid flow rate (or fluid flowspeed) may involve detecting time delays (e.g., between upstream anddownstream signals) in the range of nano-seconds.

The ADC 155 can be coupled to the processor 151 or a memory associatedwith the control circuit 150. For instance, the ADC 155 can providesignal samples directly to the processor 151 or store the samples in amemory accessible by the processor 151. The control circuit 150 canfurther include a digital-to-analog converter (DAC) configured toconvert waveform samples into analog signals. For instance, the DAC canconvert samples of a digital excitation signal into a respective analogexcitation signal that is provided as input to the ultrasonictransducer(s) 110. The processor 151 or a memory associated with thecontrol circuit 150 can store the samples of the digital excitationsignal. The ADC 151 can be capable of operating as an ADC and a DAC. Thedigital excitation signal can include a pseudo random noise, a pulsetrain with a given frequency, pure tone at a given frequency, liner orlogarithmic chirp signal or frequency modulated pulse train (e.g., withincreasing or decreasing frequency). In response to the input analogexcitation signal, the transducer 110 can output a band-pass signal thatis transmitted into the pipe 10.

The processor 151 can be configured to control the operation and timingof the ultrasonic transducers 110 (e.g., initiate transmission/receptionof ultrasonic signals 101), control the operation of the ADC 155 (e.g.,initiate signal sampling by the ADC 155), control the operation of oneor more other components of the control circuit 150, initiate and mangecommunication with other devices, execute processes for estimatingrelative time delays between distinct signals or estimating fluid flowrate, managing power consumption of the flow meter system 100 or acombination thereof. The processor 151 can include one or more of amicroprocessor, microcontroller, digital signal processor (DSP), andapplication-specific integrated circuit (ASIC). The control circuit 150can also include communication circuit(s) or component(s) forcommunicating with other devices, one or more signal amplifiers, orother analog or digital circuitry.

FIG. 2 is a flow diagram illustrating a method 200 for estimating fluidflow rate or fluid flow velocity. Referring to FIGS. 1 and 2, the method200 can include the ultrasonic transducers 110 transmitting one or moreTX signals (stage 210) and receiving one or more respective RX signals(stage 220). The method 200 can include the ADC 155 sampling the one ormore RX signals according to a first sampling rate (stage 230), and theprocessor 151 generating at least one high resolution RX signal based onsamples of the one or more RX signals provided by the ADC 155 (stage240). The at least one high resolution RX signal corresponds to a secondsampling rate higher than the first sampling rate. The method 200 canalso include the processor 151 computing, for each of the at least onehigh resolution RX signals, a respective cross-correlation signalbetween that high resolution RX signal and a waveform (stage 250). Themethod 200 can also include the processor 151 estimating fluid flow rate(or fluid flow speed) based on the computed cross-correlation signal(s)(stage 256).

The method 200 can include the transducers 110 transmitting one or moreTX signals (stage 210) and receiving one or more respective RX signals(stage 220). The ultrasonic transducers 110 can transmit (such asresponsive to instruction(s) or excitation signal(s) from the processor151) one or more downstream signals, one or more upstream signals, or acombination thereof. The ultrasonic transducers 110 can transmit aplurality of copies or versions of a TX signal and receive a pluralityof respective RX signals over a given time period. The plurality ofcopies or versions of the TX signal can include signals transmittedupstream, signals transmitted downstream, or a combination thereof. Thegiven time period can be in the range of hundreds of micro seconds (m),milli-seconds (ms) or any other time period during which channelcharacteristics are not expected to vary. The media (e.g., the pipe 10,the fluid, the waveguides, or a combination thereof) through which theultrasonic signals propagate from one transducer to another can beviewed as a communication channel whose characteristics may vary, forinstance, due to temperature variation of the media. The redundancyassociated with the plurality of received RX signals corresponding tothe plurality of transmitted copies or versions of the TX signal allowsfor noise reduction, for instance, by using averaging methods whenestimating relative signal time delays (or differences between signalpropagation times). The ultrasonic transducers 110 can transmit aplurality of copies of the TX signal that are synchronized with respectto the ADC clock signal. For instance, all the copies of the TX signalcan have the same fractional (or differential) time delay (i.e., amountof delay modulo the ADC sampling period T) with respect to the ADC clocksignal. In some implementations, the ultrasonic transducers 110 cantransmit a plurality of versions of the TX signal having distinctfractional (or differential) time delays (i.e., amount of delay modulothe ADC sampling period T) with respect the ADC clock signal. Theprocessor 151 can provide the same excitation signal as input to thetransducer 110 to generate synchronized copies of the same TX signal orprovide delayed versions (such as with distinct time delays) of anexcitation signal as input to the transducer 110 to generate delayedversions of the same TX signal.

FIG. 3 is a diagram illustrating different implementations of copies orversions of a transmit (TX) signal for transmission within a given timeperiod. According to a first scenario, the transducer 110 can transmitconsecutively three (or any other number of) copies 301 a, 301 b and 301c of the TX signal having the same fractional (or differential) timedelay (e.g., zero fractional time delay) with respect to the risingedges of the ADC clock signal 310. As such, the relative transmissiontime delay between any two of the three copies 301 a, 301 b and 301 c ofthe TX signal can be a multiple of the period T (such as k×T where k isan integer) of the ADC clock signal 310.

According to a second scenario, the transducer 110 can transmit three(or any other number of) versions 302 a, 302 b and 302 c of the TXsignal having distinct deterministic fractional (or differential) timedelays with respect to rising edges of the ADC clock signal 310. Forinstance, the fractional time delays can be

$0,{\frac{T}{3}\mspace{14mu} {and}\mspace{14mu} \frac{2T}{3}}$

resulting in linear fractional (or differential) time delays. If N (N isan integer) versions of the TX signal are transmitted over the givenperiod of time, the corresponding fractional time delays with respect tothe rising edges of the ADC clock signal 310 can be equal to

$0,\frac{T}{N},\frac{2T}{N},\ldots \;,{\frac{\left( {N - 1} \right)T}{N}.}$

As will be discussed below, the processor 151 can employ knowledge ofthe deterministic fractional (or differential) time delays for thetransmitted versions (e.g., versions 302 a, 302 b and 302 c) of the TXsignal and the corresponding received RX signals to generate the highresolution RX signal. The transmitted versions 302 a, 302 b and 302 c ofthe TX signal can propagate through the fluid (between the transducers110) over non-overlapping time intervals. For instance, the transmittimes associated with the transmitted versions (e.g., versions 301 a,302 b and 302 c) of the TX signal can be equal to t

${t + \frac{T}{N} + {kT}},{t + \frac{2T}{N} + {2{kT}}},\ldots \;,{t + \frac{\left( {N - 1} \right)T}{N} + {\left( {n - 1} \right){{kT}.}}}$

Even though the transmitted versions of the TX signal arenon-overlapping in time, the fractional (or differential) time delays

$0,\frac{T}{N},\frac{2T}{N},\ldots \;,\frac{\left( {N - 1} \right)T}{N}$

are uniformly spaced apart from each other within the ADC clock signalperiod T (or ADC sampling period). In some implementations, thefractional (or differential) time delays can be non-uniformly spacedwithin the period T.

According to a third scenario, the transducer(s) 110 can transmit three(or any other number of) versions 303 a, 303 b and 303 c of the TXsignal with distinct respective random time delays (e.g., jitteringdelays) α₁, α₂ and α₃ with respect to rising edges of the ADC clocksignal 310. The processor 151 can generate the values for α₁, α₂ and α₃as instances of a random variable (such as a uniform random variable,Gaussian random variable, Ki-squared random variable or other randomvariable). In general, the processor 151 can generate N jitter timedelays α₁, α₂, . . . , α_(N) as N instances of a random variable for Nrespective versions of the TX signal to be transmitted within the giventime period. In some implementations, applying jitter delays to thetransmission times of the versions of the TX signal helps mitigateerrors, such as errors due to finite precision computing, in respectivemeasured (or estimated) propagation times.

FIGS. 4A-4C show simulation results illustrating behavior ofdifferential propagation times between downstream and upstream TXsignals in a zero-flow fluid with and without jitter delays. The y-axisin FIGS. 4A-4C represents the differential propagation time betweendownstream and upstream signals and the x-axis represents the averagepropagation time for downstream and upstream signals. The differentialpropagation time is the measured time difference between downstreampropagation time and upstream propagation time for a respective pair oftransmitted signals including a downstream and upstream signals.

FIG. 4A shows simulation results for downstream and upstream signalswith no jitter delays applied. FIG. 4B shows simulation results fordownstream and upstream signals with jitter delays between 0 and 25 nsapplied. FIG. 4C shows simulation results for downstream and upstreamsignals with jitter delays between 0 and 250 ns applied. For allsimulation results in FIGS. 4A-4C, the downstream and upstreampropagation times are associated with non-moving fluid (i.e., with flowrate equals 0 gallons per minute (GPM)). In zero-flow (i.e., stillfluid) condition, one would expect recorded differential propagationtimes to be equal to zero. However, due to signal noise andcomputational errors, the recorded differential propagation times maynot be exactly zero. By comparing the results in FIGS. 4A-4C, one cansee that when no jitter delays are applied to the transmission times (asshown in FIG. 4A), the recorded differential propagation times exhibitrelatively (e.g., compared to results in FIGS. 4B and 4C) largerdeviations from zero. Also, as the average signal propagation timeincreases (i.e., increase along x-axis), the recorded differentialpropagation times exhibit a cumulative oscillation behavior around zero.However, when jitter delays are applied (as shown in FIGS. 4B and 4C),the recorded differential propagation times become closer to zeroimplying smaller respective errors. Also, while the results shown inFIG. 4B still show relatively larger errors and a cumulative oscillationbehavior around zero as the average signal propagation time increases,the results shown in FIG. 4C illustrate an even smaller error with nooscillation behavior. As illustrated through the simulation resultsshown in FIGS. 4A-4C, the jitter delays applied to the transmissiontimes of the transmitted versions of the TX signal mitigate the errorsin the measured differential propagation times between downstream andupstream signals, and therefore allow for more accurate estimation ofthe propagation times and the differential propagation times of thetransmitted versions of the TX signal.

Referring again to FIG. 3, according to a fourth scenario, thetransducer(s) 110 can transmit three (or any other number of) versions304 a, 304 b and 304 c of the TX signal with respective time delays(with respect to rising edges of the ADC clock signal 310) defined asaccumulations of deterministic and jitter delays. For instance, thefractional time delays associated with the versions 304 a, 304 b and 304c of the TX signal (with respect to rising edges of the ADC clock signal310) can be equal to

$\alpha_{1},{\alpha_{2} + {\frac{T}{N}\mspace{14mu} {and}\mspace{14mu} \alpha_{3}} + \frac{2T}{N}},$

respectively. For N transmitted versions of the TX signal, therespective fractional time delays can be equal to

$\alpha_{1},{\alpha_{2} + \frac{T}{N}},{\alpha_{3} + \frac{2T}{N}},\ldots \;,{\alpha_{N} + {\frac{\left( {N - 1} \right)T}{N}.}}$

As such, each fractional time delay associated with a respectivetransmitted version of the TX signal is an aggregation of adeterministic time delay value

$\left( {{e.g.},\frac{nT}{N},} \right.$

where n is an integer between 0 and N−1) and a jitter time delay value(e.g., α_(i) where i is an index between 1 and N).

In some implementations, the processor 151 can apply the above describedtime delays to an excitation signal provided as input to thetransducer(s) 110, and in response, the transducer(s) 110 can generatecorresponding TX signals with the same time delays applied to thecorresponding excitation signal. While the scenarios shown in FIG. 3 aredescribed with respect to time delays, the same scenarios can beimplemented by applying phase shifts in the frequency domain. That is,instead of applying time delays to the excitation signals, the processor151 can add phase shifts to the versions of the excitation signal in thefrequency domain. The phase shifts can be deterministic phase shifts(i.e., corresponding to the second scenario), jitter phase shifts(corresponding to the third scenario) or a combination thereof(corresponding to the fourth scenario). The processor 151 can use fastFourier transform (FFT) to transform the excitation signal to thefrequency domain and inverse fast Fourier transform (IFFT) to transformphase-shifted versions of the excitation signal back to the time domain.In some implementations, the control circuit 150 can store a copy of theexcitation signal and/or copies of the respective phase-shifted versionsin the frequency domain in order to avoid repetitive FFT and/or IFFTcomputations. While the fractional time delays described above withrespect to FIG. 3 are defined with respect to rising edges of the ADCclock signal 310, such fractional time delays can be defined withrespect down edges or other references associated with the ADC clocksignal 310.

The method 200 can include the ADC 155 sampling each of the received RXsignals at a first sampling rate R₁ (stage 230). For instance, thesampling rate R1 can be associated with a sampling period equal to ADCclock period T or a multiple thereof. The ADC 155 can be coupled to theultrasonic transducers 110 and configured to receive the RX signalsdirectly from the transducers 110. In some implementations, an amplifiercan amplify the received RX signals before the sampling process. Uponsampling the received RX signals, the ADC 155 can provide the respectivesamples to the processor 151 or a memory accessible by the processor151. In some implementations, the first sampling rate R₁ can be smallerthan a desired fine signal resolution (or a desired second sampling rateR_(d)). For instance, the first sampling rate can be in the range ofhundreds of Mega Hertz (MHz) whereas the desired fine signal resolutioncan be associated with a second sampling rate in the range of Giga Hertz(GHz).

Referring back to FIG. 2, the method 200 can include the processor 151generating, based on the samples of received RX signals, at least onerespective fine resolution RX signal associated with a second samplingrate R_(d) higher than the first sampling rate R₁. Given the first anddesired sampling rates R₁ and R_(d), the processor 151 can determineresolution factor rf

$\left( {{{such}\mspace{14mu} {as}\mspace{14mu} {rf}} = {\left\lfloor \frac{R_{d}}{R_{1}} \right\rfloor \mspace{14mu} {or}\mspace{14mu} \left\lceil \frac{R_{d}}{R_{1}} \right\rceil}} \right).$

The processor 151 can then generate the fine resolution RX signal(s)based on the resolution factor rf and samples of the received RXsignal(s).

FIG. 5 is a diagram illustrating a process of interleaving samples frommultiple received RX signals to generate a respective higher resolutioninterleaved signal. For instance, the ultrasonic transducers 110 cantransmit multiple copies of the TX signal with linear (or non-linear)incremental fractional time delays with respect to the ADC clock signal(for instance, as discussed with respect to the second scenario of FIG.3). In the example shown in FIG. 5, a first transducer 110 can transmittwo versions of the TX signal with fractional time delays equal to 0 and

$\frac{T}{2},$

respectively. A second transducer 110 can receive the respective RXsignals and an amplifier associated with the control circuit 150 canamplify the received RX signals. The ADC 155 can then sample theamplified RX signals at a first sampling rate (e.g., equal to 4 MHz).The samples of the first RX signal 501 a and the samples of the secondRX signal 501 b are out-of-sync by

$\frac{T}{2}.$

The processor 151 can interleave the samples of the first and second RXsignals 501 a and 501 b to generate a respective higher resolutioninterleaved resolution RX signal 502 with a respective effectivesampling rate equal to (e.g., 8 MHz) twice the first sampling rate ofthe ADC 155. While the example illustrated in FIG. 5 shows interleavingof samples from two distinct RX signals (such as RX signals 501 a and501 b), any number of RX signals can be employed to generate theinterleaved signal 502.

In some implementations, the processor 151 can cause the firsttransducer 110 to transmit a number of versions of the TX signal equalto the resolution factor rf with respective incremental fractional timedelays (or corresponding incremental phase shifts). The processor 151can then interleave the samples of the respective rf received RX signalsto generate a fine resolution RX signal with a second sampling rateR₂=rf·R₁. The incremental time delays can be incremental deterministictime delays (as discussed with respect to the second scenario of FIG. 3)or a combination of incremental deterministic time delays and jittertime delays (as discussed with respect to the fourth scenario of FIG.3).

FIG. 6 is a diagram illustrating a process of up-sampling a digitalsignal associated with one or more ADC-sampled RX signals to generate arespective higher resolution up-sampled RX signal. The input digitalsignal 601 to be up-sampled can be a single ADC-sampled RX signal aninterleaved signal generated by interleaving samples from multiplereceived RX signals (for instance as discussed above with regard to FIG.5). The processor 151 can insert zeros into an input digital signal 601(block 610). For instance, if the input digital signal 601 is a sampledRX signal, for each sample of the sampled RX signal, the processor 151can insert rf−1 zeros (such as preceding or following the originalsample). The processor 151 can then interpolate the samples of thezero-padded signal using a low pass filter or a transfer functionthereof (block 620) to generate the fine resolution signal 602. In someimplementations, the transfer function of the low-pass filter 605 can bea truncated sinc function. For instance, the transfer function 605 canbe a truncated sinc function including a single lobe (i.e., the mainlobe of the sinc function), truncated sinc function including threelobes or other truncation of the sinc function. In some implementations,the zero-padding at block 610 and the interpolation at block 620 can beimplemented as a single filtering operation. In some implementations,other functions (such as a triangular function, or a truncated Gaussianfunction) can be employed for interpolation. In some implementations,the processor 151 can insert, for each signal sample of the inputdigital signal 601, rf−1 copies of that sample instead of employing zeropadding.

FIG. 7 shows experimental results for measured differential propagationtimes using up-sampled RX signals. The experimental results aregenerated based on a ¾ inch CPVC (Chlorinated Polyvinyl Chloride) pipe,1 MHz ultrasonic transducers and 4 MHz ADC. The experimental resultsshown in plots (a)-(c) include 200 differences in propagation times(between downstream and upstream signals) measured for various flowrates. The continuous lines represent the average difference inpropagation time (computed by averaging the measured differences inpropagation time values at respective fluid flow rates) as a function ofthe fluid flow rate. The difference in propagation time values aremeasured by cross-correlating the up-sampled RX signals with a referencewaveform having a respective sampling rate of 4 MHz.

With respect to the experimental results shown in plot (a), the receivedRX signals are zero-padded to achieve an up-sampling rate of 256 but nointerpolation is applied when generating the respective up-sampled (orfine resolution) RX signals. The corresponding mean-square error (MSE)for the average difference in propagation times shown in the plot (a) is0.006. With respect to the experimental results shown in plot (b), theRX signals are zero-padded and an interpolation based on azero-order-hold filter is then applied to the zero-padded signal toachieve an up-sampling rate of 256. The corresponding MSE is 0.0009975.With respect to the experimental results shown in plot set (c), thereceived RX signals are zero-padded and an interpolation based on atruncated sinc function with a single lobe is then applied to thezero-padded signal to achieve an up-sampling rate of 256. Thecorresponding MSE is 0.0001623. The computed MSEs illustrate that moreaccurate estimations of the differential propagation times can beachieved when using the truncated sinc function (e.g., with 512 samples)for interpolation compared to the case where no interpolation is applied(plot (a)) or an interpolation using a zero-order-hold filter is applied(plot (b)). That is, employing the truncated sinc function (e.g.,truncated to include a single lobe) for interpolation allows forsubstantial improvement in terms of the accuracy of the estimated (ormeasured) signal propagation times. Also, truncating the sinc function(or any other transfer function of a respective low-pass filter) allowsof reduction in computational complexity.

Referring back to FIGS. 2, 5 and 6, the processor 151 can generate thefine resolution signal by employing both signal interleaving (asdiscussed with regard to FIG. 5) and up-sampling (as discussed withregard to FIG. 6). Signal interleaving allows for accurately increasingsignal resolution using RX signals received over a timer period duringwhich channel characteristics do not vary (or at least do not varysignificantly). However, in some instances, such time period may not besufficient to transmit rf non-time-overlapping TX signals (and inresponse receive rf corresponding RX signals). For instance, if the timeperiod during which channel characteristics are substantiallynon-varying is 5 ms and the time duration for transmitting each signalis 0.1 ms, the flow meter system can use at most 50 RX signals forinterleaving to achieve an interleaved signal with effective samplingrate equal to 50 times the sampling rate of the RX signals. If theresolution factor rf is larger than 50 (such as rf=256), the flow metersystem 100 can further apply up-sampling (as discusses with regard toFIG. 6) to an interleaved signal to generate a fine resolution RX signalwith the desired resolution R_(d). Also, in some instances, the ADCsampling rate may be smaller than the Nyquist rate. In such instances,signal interleaving can be employed to avoid aliasing. The interleavedsignal(s) can then be up-sampled to generate the fine resolution signalwith desired resolution R_(d).

Referring back to FIG. 2, the method 200 can include computing a crosscorrelation signal between the fine resolution RX signal and a referencewaveform (stage 250) and determining a difference in propagation timebetween the reference waveform and the fine resolution RX signal. Thereference waveform can be a representation (e.g., a sampled version) ofan upstream RX signal, downstream RX signal, zero-flow RX signal (i.e.,a RX signal received when the fluid flow rate is zero), TX signal, or awaveform derived therefrom. For instance, if the fine resolution RXsignal is generated based on one or more downstream RX signals, thereference waveform can be an upstream RX signal or a zero-flow RXsignal. If the fine resolution RX signal 502 or 602 is generated basedon one or more upstream RX signals, the reference waveform can beassociated with a downstream RX signal, a zero-flow RX signal or therespective TX signal. In some instances, the processor 151 can producethe reference waveform by filtering the TX signal (or the respectiveexcitation signal) using a filter configured to model signal distortionsinduced by the transducers 110, the pipe 10, the fluid, the amplifier(if any), the ADC 155, the waveguides 120, or a combination thereof.

In some implementations, the reference waveform can be a sine wave orother narrowband signal. In such implementations, the processor 151 cancompute a first cross correlation signal representing cross correlationbetween an upstream RX signal and the sine wave (or the narrowbandsignal), and a second cross correlation signal representing crosscorrelation between a downstream RX signal and the sine wave (or thenarrowband signal). Using the first and second cross correlationsignals, the processor 151 can determine a difference in signalpropagation time between the upstream signal and the downstream signal.The processor 151 can determine such difference in signal propagationtime based on a time shift between the first and second crosscorrelation signals. For instance, the processor can determine the timeshift as the time shift between two local maxima (or two local minima ortwo zero crossings) associated with the first and second crosscorrelation signals, respectively. In some instances, the first andsecond cross correlation signals can be associated with an upstream RXsignal and a zero-flow signal (or a zero-flow signal and a downstreamsignal).

In some implementations, the processor 151 can filter two RX signals(such as an upstream and a downstream RX signals, a zero-flow and anupstream signals, or a downstream and a zero-flow RX signals) using anarrowband filter and then compute a cross correlation signal betweenthe filtered signals. In such implementations, one of the filtered RXsignals acts as the reference waveform. Applying band-pass filtering, orusing a narrowband signal (such as a sine waveform) as the referencewaveform, allows for estimating the difference in signal propagationtime with respect to narrow components of the RX signal(s). Suchapproach provides better accuracy, especially if the ultrasonic signalspeed in the fluid (or across the pipe wall 11) varies in terms offrequency. Using narrowband components of received RX signals allows formitigation of any errors, in estimating the difference in signalpropagation time, due to signal speed variation as a function of signalfrequency.

The reference waveform can have a respective resolution corresponding tothe first sampling rate, the second sampling rate or a sampling rate inbetween. Computing a full cross-correlation signal (e.g., including allcross correlation values based on the samples of the fine resolutionsignal and the reference waveform) is computationally demanding as itinvolves a huge number of multiplications. FIGS. 8A-D illustrateprocesses for estimating time shifts between distinct signals based onefficient computations of cross correlation values.

FIG. 8A shows a block diagram illustrating a process 800 of estimating atime shift between a reference waveform and a fine resolution RX signalbased on partial cross-correlation signal(s). The processor 151 can beconfigured to compute a cross-correlation signal based on an inputsignal 801 generated based on one or more RX signals and a firstreference waveform 805. The input signal 801 can be a received RX signal(downstream or upstream), up-sampled version of a received RX signal,interleaved version of two or more received RX signals, a narrowbandfiltered version of a RX signal, or other signal representative of oneor more RX signals. The fine resolution signal 802 can represent a fineresolution version of the input signal 802, a fine resolution version ofone or more RX signals, or a fine resolution version of one or morenarrowband filtered RX signals. The effective sampling rate of the inputsignal 801 can be a rate ranging between R₁ to R_(d).

The second reference waveform 807 can be a sampled zero-flow RX signal(or a narrowband filtered version thereof), a sampled upstream RX signal(or a narrowband filtered version thereof), a sampled downstream RXsignal (or a narrowband filtered version thereof), an interleaved and/orup-sampled version of a RX signal (or a narrowband filtered versionthereof), a sine wave, or a narrowband signal, while the first referencewaveform 805 can be a truncated, down-sampled or trimmed version of athe second reference waveform 807. For instance, the first referencewaveform 805 can be produced by nullifying (e.g., forcing to be zero)the samples of the second reference waveform 807 with respectiveamplitudes that are smaller than a given threshold value. Such thresholdvalue can be equal to 90%, 95% or other percentage of the peak samplevalue of the second reference waveform 807. In some implementations, thefirst reference waveform 805 can be defined as a portion of the secondreference waveform 807 associated with a respective time window. Forinstance, samples of the first reference waveform 805 can be equal torespective samples of the second reference waveform 807 within the giventime window and equal to zero outside the given time window. The timewindow can be selected (or defined) to capture the high energy samples(such as around the peak value) of the second reference waveform 807.The first and second reference waveforms 805 and 807 can be generatedduring calibration of the flow meter system 100. The first and secondreference waveforms 805 and 807 can be generated on the fly based on oneor more received RX signals. In some instances, the fine resolutionsignal 802 can be representative of one or more down-stream RX signalsand the first and second waveforms 805 and 807 can be generated based onone or more upstream RX signals (or vice versa). Using truncated,down-sampled, or trimmed version of a received RX signal (or of a signalrepresentative of one or more RX signals) allows for reduction incomputational complexity when computing the first cross-correlationsignal.

The processor 151 can then determine a first estimate of the differencein signal propagation time associated with two distinct RX signals basedon the computed first cross-correlation signal (block 810). For example,if the first reference waveform 805 is a representation of a RX signal,the processor 151 can compute the first estimate of the difference insignal propagation time as the time shift between the first referencewaveform 805 and the input signal 801 based on the correlation signalcomputed using the first reference waveform 805 and the input signal801. However, if the first reference waveform 805 is a sine wave or anarrowband signal, the processor 151 can compute a cross correlationsignal using a first input signal 801 (e.g., representing a downstreamRX signal) and the first reference waveform 805, and another crosscorrelation signal using a second input signal 801 (e.g., representingan upstream RX signal) and the first reference waveform 805. Theprocessor can then determine a first estimate of the difference insignal propagation time associated with the first and second inputsignals 801 as the time shift between the computed cross correlationsignals. In some implementations, instead of computing a coarse estimateof the time shift between the input signal 801 and the first inputreference waveform 805, the processor 151 can identify a reference point(e.g., a local or global maximum, a local or global minimum, or a zerocrossing) associated with the based on the correlation signal computedusing the first reference waveform 805 and the input signal 801.

The first estimate of the difference in signal propagation time (or theidentified reference point(s)) can be used to determine an accurateestimate of the difference in signal propagation time between the fineresolution signal 802 and the second reference waveform 807 (or two fineresolution signals 802 associated with two input signals 801 where thesecond reference waveform 807 is a sine wave or a narrowband signal).The processor 151 can locate a global or local maximum, a global orlocal minimum, or a zero crossing of a first cross-correlation signalcomputed using the first reference waveform 805 and an input signal 801,as an initial guess to determine a more accurate position of acorresponding global or local maximum, a corresponding global or localminimum, or a corresponding zero crossing in a second cross-correlationsignal computed using the second reference waveform 807 and a highresolution signal 802. In order to determine an accurate estimate of thedifference in signal propagation time between the fine resolution signal802 and the second reference waveform 807 (or two fine resolutionsignals 802 where the second reference waveform 807 is a sine wave or anarrowband signal), the processor 151 can compute a secondcross-correlation signal (e.g., a partial cross-correlation signal)using the fine resolution RX signal 802 and the second referencewaveform 807. In computing the second cross-correlation signal, theprocessor 151 can compute respective samples associated with aneighborhood of a reference point in the second cross-correlation signalcomputed using the fine resolution RX signal(s) 802 and the secondreference waveform 807. In other words, the processor 151 can compute asubset of the samples of the second cross correlation signal around thereference point. The reference point can be determined based on acorresponding reference point associated with the firstcross-correlation signal computed using the input signal 801 and thefirst reference waveform 805.

FIG. 8B shows an illustration of the first and second cross correlationsignals 830 and 840. The processor 151 can determine a first referencepoint 832 associated with (such as the peak of) the firstcross-correlation signal 830 and use the first reference point 832 todetermine a second reference point 842 (such as a local maximum)associated with the second cross-correlation signal 840. In someimplementations, the processor 151 can employ an offset value 835 (e.g.,determined during calibration of the flow meter system 100) to determinethe second reference point 842 based on the first reference point 832.In some implementations, the processor 151 can then determine a timewindow 846 based on the second reference point 842 and can computesamples of the second cross-correlation signal 840 associated withinthat time window 846. The time window 846 can be centered at (orincluding) the second reference point 842. By using the time window 846,the processor 151 can compute a relatively small number ofcross-correlation values when computing the second cross-correlationsignal.

In order to determine an accurate estimate of the difference in signalpropagation time, the processor 151 can then search for a local maximum(or other feature such as a local minimum or zero crossing) of thesecond cross-correlation signal 840 based on the time window 846 (block820 of FIG. 8A). In some implementations, the time window 846 can bedefined to include a single local maximum regardless of its locationwithin the second cross-correlation signal 840. The processor 151 candetermine the time shift between the fine resolution RX signal 802 andthe second reference waveform 807 (or between two fine resolutionsignals 802 where the second reference waveform 807 is a sine wave or anarrowband signal) based on the determined local maximum (or otherfeature) of the second cross-correlation signal 840. For instance, ifthe local maximum value is the cross-correlation sample generated asΣr(n)·f(n+τ) where r(n) is the second reference waveform 807 and f(n) isthe fine resolution RX signal 802, then τ is the time delay between thefine resolution RX signal 802 and the second reference waveform 807.However, where the second reference waveform 807 is a sine wave or anarrowband signal, the processor 151 can determine the time shiftbetween two fine resolution signals 802 as the time shift betweencorresponding local maxima (or local minima) in two cross correlationsignals computed between the two fine resolution signals 802 and thesecond reference waveform 807. In some implementations, the processor151 can be configured to slide the time window 846 (and repeat searchingfor the local maximum) if the respective local maximum (or otherreference feature) is determined to be on a boundary of the time window846.

FIG. 8C shows a cross-correlation plot and a state machine diagramillustrating a process for determining a cross-correlation feature value(such as local maximum or local minimum) associated with a respectivetime window 846. Given the time window 846, the processor 151 cancompute all cross-correlation values within the time window 846. Asdiscussed above with respect to FIG. 8B, the processor 151 can definethe time window 846 based on a first reference point 832 associated withthe first cross-correlation signal 830. The processor 151 can locate afeature value (such as local maximum or local minimum) within the timewindow 846. If the value is not on the boundary of the time window 846(not at L or R), the processor 151 can stop the search process and usethe determined location of the feature value to determine the time delaybetween the fine resolution RX signal 802 and the second referencewaveform 807. If the location of the feature value is determined to beat the right boundary (at point R) of the time window 846, the processor151 can shift the time window 846 to the right and restart the searchprocess for the feature value. If the location of the feature value isdetermined to be at the left boundary (at point L) of the time window815, the processor 151 can shift the time window 846 to the left andrestart the search process. Shifting the time window 846 can includecomputing additional cross-correlation values (e.g., not previouslycomputed). As shown in the state machine diagram, the processor 151 canstop the search process if the cross-correlation peak is determined tobe located (i) not on a boundary point of the time window 846, (ii) onthe right boundary point of the time window 846 after a left-shift or(iii) on the left boundary point of the time window after a right-shift.

FIG. 8D is a diagram illustrating a ternary search for locating afeature value (such as local maximum or local minimum) within a timewindow 846. The processor can be configured to segment the time window846 into three overlapping time segments; a left segment 847, a centersegment 848 and a right segment 848. In some implementations, the timewindow 846 can have a length equal to an up-sampling factor UF (orresolution factor rf) associated with the fine resolution RX signal 802.The processor 151 can compute and compare cross-correlation values at amiddle point P and boundaries points L and R of the center segment 848.

If the cross-correlation value associated with the left boundary point Lis determined to be the largest (among three computed values), theprocessor 151 can sub-divide the time left segment 847 into threerespective overlapping sub-segments (similar to segmentation of timewindow 846). The processor 151 can then compare the cross-correlationvalues associated with the middle and boundary points of the middlesub-segment within the left segment 847 (similar to points L, P and R ofsegment 848). If the cross-correlation value associated with the rightboundary point R is determined to be the largest (among three computedvalues), the processor 151 can sub-divide the right segment 849 intothree respective overlapping sub-segments (similar to segmentation oftime window 846). The processor can then compare the cross-correlationvalues associated with the middle and boundary points of the middlesub-segment within the right segment 849 (similar to points L, P and Rof segment 848). If the cross-correlation value associated with themiddle point P is determined to be the largest (among three computedvalues), the processor 151 can then segment the center segment 848 intothree overlapping sub-segments and apply the same search process to thethree sub-segment. That is, the processor 151 can compute crosscorrelation values associated with the middle and boundary points of thecenter sub-segment and compare such values to determine which segment isto be further sub-divided in smaller segments.

The processor 151 can repeat the process described above until thecenter sub-segment cannot be segmented any further, in which case thelocation of the largest cross-correlation value determined through thesearch process is checked. If the largest cross-correlation value (foundby the ternary search process) is found to be smaller any of thecross-correlation values at the boundary points (such as at 0 or UF−1)of the original time window 846, the processor 151 can shift the timewindow 846 towards the boundary point (such as to the left or to theright) with the largest cross-correlation value and repeat the ternarysearch process for the shifted time window. If the largestcross-correlation value (determined by the ternary search process) isfound to be greater than both cross-correlation values at the boundarypoints (such as at 0 or UF−1) of the original time window 846, theprocessor 151 can use the largest cross-correlation value determined bythe ternary search process as the local maximum. In someimplementations, the processor 151 can be configured to storecross-correlation values computed at each stage of the ternary searchprocess to avoid repetitive computing of a given cross-correlationvalue.

The processes discussed with regard to FIGS. 8A-8D allow forcomputationally efficient estimation of the time delay between the fineresolution RX signal 802 and the second reference waveform 807. Inparticular, the discussed processes allow for significant reduction inthe number of cross-correlation values computed even when fineresolution RX signals are employed. Also, the processor 151 can beconfigured to compute the first cross-correlation signal 830 only once.Once the respective first reference point 832 is determined, theprocessor 151 can use it for all subsequent fine resolution signals 802to determine the time window 846. For instance, if the first referencepoint 832 is determined using an input signal 801 corresponding to arespective downstream RX signal, the processor 151 can use the samereference point (without re-computing the first cross-correlation signal830) for subsequent downstream or up-stream RX signals to determine therespective time window 846.

In some implementations, the processor 151 can be configured to computeseveral estimates of the time delays between a plurality of received RXsignals (e.g., including downstream and/or up-stream RX signals) andrespective reference waveform(s) 807. When jitter delays are employed(as discussed with regard to FIG. 3), the processor 151 can beconfigured to take the added delay into consideration when determiningthe second reference point 842 based on the first reference point 832.The processor 151 can also be configured to average signal propagationtimes estimated based on two or more RX signals (e.g., associated withdistinct jitter delays) to produce a final estimate of the signalpropagation time.

Referring back to FIG. 2, the processor 151 can determine the fluid flowrate (or fluid flow speed) based on the determined time shift betweenthe fine resolution RX signal 802 and the reference waveform or betweentwo cross correlation signals associated with two fine resolutionsignals 802 (stage 260). The processor 151 can employ a lookup table ora formula to compute the fluid flow rate (or fluid flow speed). Forinstance, water flow rate is proportional to differential propagationtime between downstream and upstream signals. The processor 151 can haveaccess to a data structure (e.g., a lookup table) mapping time delaysbetween RX signals and the reference waveform to corresponding fluidflow rates (or fluid flow speeds). In some implementations, the mappingcan be dependent on the temperature of the fluid or the lumen. Forinstance, the fluid flow meter system 100 can include (or be couple to)a thermostat for measuring the temperature of the environment, the lumenor the fluid therein. In some implementations, the processor 151 cancompute the fluid flow rate (or fluid flow velocity) based on amathematical formula correlating differential propagation times tocorresponding fluid flow rates (or fluid flow velocities).

FIG. 9 shows a block diagram illustrating another method for estimatingfluid flow rate (or fluid flow velocity) based on recorded ultrasonicsignals. The processor 151 can cross-correlate (block 910) a first RXsignal (e.g., a downstream RX signal) 901 a with a reference waveform907 that is generated based on a second RX signal (e.g., an upstream RXsignal) 901 b. In some implementations, the first and second RX signals901 a and 901 b are sampled at the first sampling rate (e.g., thesampling rate of the ADC 155). In some implementations, the processor151 can produce the reference waveform 907 by applying a windowoperation to the second RX signal 910 b. That is, the reference waveform907 represents a portion of the second RX signal 901 b that isassociated with a time window 950. The processor 151 can then up-samplethe cross-correlation computed based on the first RX signal 901 a andthe reference waveform 907 by applying zero-padding (bock 920) followedby interpolation, for instance, using a truncated sinc function (block93). The processor 151 can then locate the maximum of thecross-correlation signal to determine the relative time delay (ordifferential signal propagation time) between the first and second RXsignals 901 a and 901 b. In some implementations, the processor 151 canapply a window search process (e.g., as discussed with regard to FIG.8C) to locate the cross-correlation peak. In some implementations, thefirst RX signal 901 can be an upstream RX signal and the second RXsignal can be a downstream signal. In some implementations, the first RXsignal 901 a can be a downstream or upstream signal while the second RXsignal can be zero flow RX signal.

Compared to the method described in FIG. 2, the method described in FIG.9 does involve generating a fine resolution RX signal. Thecross-correlation can be computed between signals sampled at thesampling rate of the ADC 155. However, the computed cross-correlationsignal can be up-sampled to achieve better estimate of the relative timedelay between the first and second RX signals 901 and 901 b.

While the systems, devices and methods in the current disclosure aredescribed in terms of ultrasonic transducers, alternative flow ratesensors can include magnetic field sensors acoustic sensors or othersensors capable of sensing other types of signals propagating through afluid in a lumen. The systems, devices and methods described in thecurrent disclosure can be used to measure flow rates in fluiddistribution systems such as water distribution systems, natural gasdistribution systems, oil distribution systems, or other fluiddistribution systems used in different industries.

While the invention has been particularly shown and described withreference to specific embodiments, it should be understood by thoseskilled in the art that various changes in form and detail may be madetherein without departing from the spirit and scope of the invention asdefined by the following claims.

1-23. (canceled)
 24. A method comprising: sampling, by a fluid flowmeter, a plurality of signals at a first sampling rate, the plurality ofsignals for measuring a fluid flow parameter of fluid flowing through alumen; generating, by the fluid flow meter, a fine resolution signalusing sampled versions of the plurality of signals, the fine resolutionsignal having a second sampling rate higher than the first samplingrate; computing a cross-correlation signal indicative ofcross-correlation between the fine resolution signal and a referencewaveform; and determining an estimate of the fluid flow parameter of thefluid based on the computed cross-correlation signal.
 25. The method ofclaim 24, wherein the fluid flow parameter includes fluid flow rate orfluid flow velocity.
 26. The method of claim 24, wherein sampling theplurality of signals includes sampling the plurality of signals withdistinct jitter delays with respect to periods of a clock signal. 27.The method of claim 26, wherein determining the estimate of the fluidflow parameter includes: determining a plurality of first estimates ofthe fluid flow parameter based on the plurality of signals sampled withdistinct jitter delays with respect to the periods of the clock signal;and generating a final estimate of the fluid flow parameter by averagingthe plurality of first estimates.
 28. The method of claim 24, whereingenerating a fine resolution signal includes up-sampling a signalassociated with the sampled versions of the plurality of signals, theup-sampling includes applying interpolation using a truncated sincfunction.
 29. The method of claim 24, wherein sampling the plurality ofsignals includes sampling the plurality of signals with distinctincremental delays with respect to periods of the clock signal.
 30. Themethod of claim 29, wherein generating the fine resolution signalincludes interleaving samples of the plurality of signals sampled withdistinct incremental delays with respect to the periods of the clocksignal.
 31. The method of claim 30, wherein generating the fineresolution signal includes up-sampling an interleaved signal generatedby interleaving the samples of the plurality of signals sampled withdistinct incremental delays with respect to the periods of the clocksignal.
 32. The method of claim 24, wherein the reference waveformrepresents a signal component associated with the plurality of signals.33. The method of claim 24, wherein the reference waveform is associatedwith a zero-flow signal.
 34. The method of claim 24, wherein computingthe cross-correlation signal includes: computing a firstcross-correlation signal between a first reference waveform and a signalassociated with the sampled versions of the plurality of signals, thefirst reference waveform different from the reference waveform and thefirst cross-correlation signal different from the cross-correlationsignal; determining a time window based on the first cross-correlationsignal; and computing the cross-correlation signal by computing aplurality of cross-correlation values within the time window andindicative of cross-correlations between the reference waveform and thefine resolution signal.
 35. The method of claim 34, wherein determiningthe time window includes: determining a first reference point associatedwith the first cross-correlation signal; determining a second referencepoint associated with the cross-correlation signal based on the firstreference point; and determining the time window based on the secondreference point.
 36. The method of claim 35 further comprisingnullifying samples of the first reference waveform that are less than athreshold value.
 37. The method of claim 35, wherein the signalassociated with the sampled versions of the plurality of signalsincludes at least one of: a sampled version of a signal of the pluralityof signals; an up-sampled version of a signal of the plurality ofsignals; an interleaved version of the sampled versions of the pluralityof signals; and the fine resolution signal.
 38. The method of claim 35,further comprising: locating a maximum cross-correlation value of theplurality of cross-correlation values within the time window; inresponse to locating the maximum cross-correlation value at a boundarypoint of the time window, shifting the time window towards that boundarypoint; and in response to locating the maximum cross-correlation valueinside the time window, determining a time delay between the referencewaveform and the fine resolution signal using a location of the maximumcross-correlation value inside the time window.
 39. The method of claim38, wherein locating a maximum cross-correlation value inside the timewindow includes applying a ternary search process.
 40. The method ofclaim 38, wherein determining the estimate of the fluid flow parameterincludes determining the estimate of the fluid flow parameter based onthe time delay between the reference waveform and the fine resolutionsignal.
 41. The method of claim 40, further includes using a lookuptable to determine the estimate of the fluid flow parameter based on thetime delay between the reference waveform and the fine resolutionsignal.
 42. The method of claim 24, wherein generating the fineresolution signal includes generating a first fine resolution signal anda second fine resolution signal based on the plurality of signals, thefirst and second fine resolution signals associated with the secondsampling rate higher than the first sampling rate; computing thecross-correlation signal includes computing a first cross-correlationsignal indicative of cross-correlation between the first fine resolutionsignal and the reference waveform and computing a secondcross-correlation signal indicative of cross-correlation between thesecond fine resolution signal and the reference waveform; anddetermining the estimate of the fluid flow parameter based on the firstand second cross-correlation signals.
 43. The method of claim 24,comprising: generating the fine resolution signal as a filtered versionof one or more corresponding signals using a bandpass filter; filteringthe reference waveform using the bandpass filter; and computing thecross-correlation signal using the fine resolution signal, generated asa filtered version of the one or more corresponding signals, and thefiltered reference waveform.